Chaos Construction: Miracle on 81 Cells
(Eingestellt am 17. September 2025, 07:00 Uhr von Playmaker6174)
This puzzle is also one of my major projects this year and specifically, it's among my three (and a half) main projects aimed towards the later half of this year, the previous works were Modern Art 2 and Liar Jsum chaos construction as an experimental form (both of which have been rather under solved for some reasons).
I briefly mentioned this project in that liar Jsum puzzle and this is easily one of the most arduous projects I've ever worked on, since I did the researches entirely by hands (some of them I haven't even finished analyzing or touched upon) and only relied on Rangsk's solver to shorten the uniqueness confirmation at different points in the setting.
Even though this didn't turn out quite as what I expected at first, I was still greatly satisfied with how the solve of this final version turned out and in fact, I felt like I might've outperformed myself with this one. For now, let's see how it goes over here:
Rules:
- Every row and column in the 9x9 grid contain digits from 1 to 9 each once. In addition, divide the entire 9x9 grid into nine orthogonally connected regions so that each region will also contain digits from 1 to 9 each once as well.
- Each clue outside a row/column/diagonal contains a unique positive integer value* that needs to be deduced, and the following properties must be satisfied:
1) The first cell and the last cell of that row/column/diagonal have different odd/even parity.
2) The clue shows the sum of two cells belonging to the two last seen regions from that clue's direction that share common side/vertices.
3) The clue shows the sum of the first X cells seen from that clue's direction in its respective row/column/diagonal, where X is the first digit seen by that clue. In addition, those X cells must belong to the same region and the (X+1)th cell next to them must belong to a different region and must also be marked with a circle in that cell.
- Whenever a cell is marked with a circle in it, its digit is equal to the amount of surrounding cells sharing the same region as that cell - including itself and counting up to nine cells. Three additional circles have been given and those three circles must contain distinct numbers to each other.**
In this puzzle, not all possible marked circles are given.
Setter's note:
(*) This means no two outside clues will have the same value to each other.
(**) This rule only applies to the three given circles, so it's possible other circles being generated by outside clues have the same number as some of those threes.
Also, here's an example image of how the entire ruleset works.
Puzzle: Penpa plus - Sudokupad
The answer check in penpa link will activate once all of the digits are correctly filled and also the region borders are correctly drawn. For now, good luck and have fun solving!
Lösungscode: Enter column 7 from top to bottom with a hyphen '-' for a region border, not counting the 9x9 grid perimeter. For example: 123 - 45 - 67 - 89.
Kommentare
am 23. November 2025, 18:21 Uhr von valacd
Great puzzle with beautiful interactions. Hard, but not too hard, very enjoyable! Thank you for this puzzle!
And thanks to WildEnte, great fun (as always)
am 23. November 2025, 15:36 Uhr von WildEnte
This was quite hard from start to finish, but also never unfair. Beautiful interactions throughout - a lovely puzzle!
As usual I could not have done it without valacd!
am 2. Oktober 2025, 09:35 Uhr von marcmees
Very hard in midsolve. I did overlook for a long time a construction possibility. What I supposed to be 2 cells of different regions finally belonged to the same one. Very beautiful. Thanks
am 23. September 2025, 15:44 Uhr von skuntsel
This is just a brilliant masterpiece from a great-great setter! Classic Playmaker6174. It belongs to one of these stunning puzzles you need to solve once in your lifetime. Super fascinating all around. Non-trivial and beautiful. Keeps your attention and resilient until the end. With a hard-mode irregular sudoku on top of everything else of course. Just hard to believe even after solving that it all resolves at all let alone that beautiful. Props to you, Playmaker6174!
am 20. September 2025, 17:09 Uhr von SeveNateNine
Amazing puzzle.
am 20. September 2025, 10:28 Uhr von Piatato
Awesome!
am 17. September 2025, 23:34 Uhr von bansalsaab
Amazing. Slow burn until almost the end.
am 17. September 2025, 21:12 Uhr von War
Beautiful logic from start to finish, with the complex ruleset making a unique puzzle out of such few clues
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Thank you for solving and the sweet comment! Happy to know that you made it to the end :)
am 17. September 2025, 07:10 Uhr von Playmaker6174
Wow, I didn't even notice the puzzle ID until finishing this post [lol]
